A structural engineer is evaluating three alternative designs on the basis of four performance measures: construction cost, structural integrity, the expected average lifetime condition (resistance to freeze and freeze-thaw cycles), and the effects of the bridge construction on the environment, each having relative importance weights of 0.3, 0.4, 0.2, and 0.1 respectively. For the overall structural integrity (OSI), the index is 0 (worst) to 5 (best); life-cycle cost is in $millions; lifetime condition is an index ranging from 0 (worst) to 20 (best); and the environmental consequences (EC) is an index ranging from 0 (best) to 50 (worst). The utility functions Uj are provided as follows:
UOSI = 16.33(OSI)
Ucost = -20.898(cost)+ 175.19 (where cost is in $millions)
Ucondition = 5(condition)
UEC = -0.1235(EC)2 + 3.0745(EC)+ 82.673
The levels of each performance criterion (PC) for material are given in the table below.
|
OSI
|
Cost
|
Condition
|
Environmental
|
|
Design A
|
3
|
7.5
|
18
|
38
|
|
Design B
|
4
|
4.0
|
11
|
25
|
|
Design C
|
3
|
5.0
|
15
|
30
|
(a) Using the basic weighted additive method of multiple criteria evaluation, determine which design should be recommended for the new structure.
(b) What must be the percentage reduction in Design A's cost for that alternative to be the optimal choice?